Download Secondary Honors Algebra II Objectives

Secondary Honors Algebra II Objectives
Chapter 1 – Equations and Inequalities
Students will learn to evaluate and simplify numerical and algebraic expressions,
to solve linear and absolute value equations and inequalities, to use algebra to
model and solve real life problems.
• Solve Linear equations and inequalities.
• Solve absolute value equations.
• Solve compound inequalities; including absolute value inequalities.
• Graph the solution sets of compound inequalities.
• Simplify problems using mathematical operations.
• Multiply polynomial expressions.
Chapter 2 Linear Equations and Functions
Students will learn to graph and write equations for linear equations and
inequalities in 2 variables, and absolute value functions.
• Use patterns, relations, and functions to represent mathematical situations.
• Compare and contrast relations and functions.
• Identify the domain and range of the absolute value, quadratic, and radical functions.
• Use function notation.
• Represent quantitative relationships using mathematical models and symbols.
• Find the vertex and axis of symmetry of an absolute value function algebraically and
graphically.
• Specify locations and describe spatial relationships using coordinate geometry
• Graph quadratic, polynomial, square and cube root, and absolute value functions.
• Transform the graphs of linear, absolute value, quadratic, and radical functions by
stretching, shifting, and reflecting.
• Graphing piecewise and step functions.
Chapter 3 Systems of Linear Equations and Inequalities
Students will learn how to solve linear systems of 2 or 3 variables by graphing
and algebraic methods and how to write and use linear systems to solve real life
problems.
• Evaluate, solve, and analyze mathematical situations using algebraic properties and
symbols.
• Solve systems of equations with three variables.
• Represent quantitative relationships using mathematical models and symbols.
• Solve real world problems using the methods for systems of 2 and 3 linear equations.
• Solve problems using visualization, spatial reasoning, and geometric modeling.
• Use linear programming to solve real life problems.
Chapter 4 – Matrices and Determinants
nd
Students will add, subtract, and multiply matrices. Students will evaluate 2 and
rd
3 order determinants. Students will solve linear systems using Cramer’s Rule
and inverse matrices.
• Simplify problems using mathematical operations.
• Evaluate 2nd and 3rd order determinants.
• Use patterns, relations, and functions to represent mathematical situations.
• Perform arithmetic operations on matrices.
• Evaluate, solve, and analyze mathematical situations using algebraic properties
and symbols.
• Solve systems of equations using Cramer’s Rule.
• Solve systems of equations using matrix equations.
Chapter 5 Quadratic Functions
Students will learn to factor quadratic polynomials. Students will learn the
complex number system and the rules for working in it. Students will learn 4
methods for solving quadratic equations and how to graph quadratic functions
and inequalities.
• Represent complex numbers in a variety of ways.
• Extend the number system to include complex numbers in a + bi form.
• Identify the use for the square root of a negative number and define the imaginary
unit.
• Simplify square roots, including those containing negative radicands.
• Simplify problems using mathematical operations.
• Add, subtract, multiply, divide, and raise complex numbers to a power.
• Evaluate, solve, and analyze mathematical situations using algebraic properties
and symbols.
• Solve quadratic equations by factoring, the Quadratic Formula, and completing the
square.
• Solve radical equations, including those with extraneous solutions.
• Solve single-variable quadratic inequalities.
• Solve quadratic inequalities in 2 variables.
• Write a quadratic equation when given the rational roots or zeros of the function.
• Represent quantitative relationships using mathematical models and symbols.
• Solve real world problems with the methods for solving quadratic equations.
• Find the vertex, maximum or minimum values, intercepts, and axis of symmetry of
a quadratic function algebraically and graphically.
• Apply the steps of factoring.
• Factor a quadratic trinomial with a leading coefficient.
• Factor using multiple steps.
• Specify locations and describe spatial relationships using coordinate geometry.
• Graph quadratic functions.
• Graph quadratic inequalities in 2 variables.
• Write the equations of functions given the graph or information about the graph.
Chapter 6 Polynomial Function
Students will learn to perform operations on polynomials. Students will learn to
evaluate, graph, and find the zeros of polynomial functions.
• Simplify problems using mathematical operations.
• Simplify numerical expressions with exponents of any degree.
• Multiply polynomial expressions with any number of terms.
• Divide polynomial expressions using synthetic and long division.
• Find the zeros of a polynomial function.
• Evaluate, solve, and analyze mathematical situations using algebraic properties
and symbols.
• Solve polynomial equations by factoring.
• Recognize that negative exponents mean reciprocals.
• Use synthetic substitution to evaluate polynomial functions.
• Apply the steps of factoring.
• Factor a sum or difference of cubes.
• Factor by grouping.
• Factor using multiple steps.
• Factor polynomials of 3rd, 4th, or 5th degree.
• Specify locations and describe spatial relationships using coordinate geometry.
• Graph polynomial functions.
Chapter 7 Powers, Roots, and Radicals
Students will learn how to use rational exponents and nth roots of numbers, how
to perform operations with and find inverses of functions, and how to graph
radical functions and solve radical equations.
• Represent complex numbers in a variety of ways.
• Simplify radical expressions of any index.
• Simplify problems using mathematical operations.
• Simplify using rational exponents.
• Use patterns, relations, and functions to represent mathematical situations.
• Find the inverse of a function by interchanging the values of domain and range,
reflecting across the line y = x, or by using algebraic methods.
• Find the compositions or combinations of two simple functions.
• Evaluate, solve, and analyze mathematical situations using algebraic properties
and symbols.
• Solve radical equations including those with extraneous roots.
• Recognize that rational exponents are used to represent radicals.
• Specify locations and describe spatial relationships using coordinate geometry.
• Graph square root and cube root functions.
Chapter 8 Exponential and Logarithmic Functions
Students will learn how to graph and use exponential, logarithmic, and logistic
growth functions. Students will learn about the number e and the properties of
logarithms. Students will learn to solve exponential and logarithmic equations.
• Represent quantitative relationships using mathematical models and symbols.
• Solve real world problems using the methods for solving exponential and
logarithmic equations.
• Understand the relationship between exponents and logarithms.
• Graph exponential and logarithmic functions.
• Apply Euler’s number and its relationship to logarithms.
• Use the laws of logarithms to simplify logarithmic expressions and solve logarithmic
equations.
• Convert logarithmic equations into exponential equations and vice versa.
• Use the laws of exponents to solve exponential equations.
Chapter 9 Rational Functions
Students will learn how to simplify and perform operations with rational
expressions, how to graph rational functions, and how to solve rational
equations.
• Evaluate solve, and analyze mathematical situations using algebraic properties and
symbols.
• Solve rational equations.
• Specify locations and describe spatial relationships using coordinate geometry.
• Graph rational functions.
Chapter 10 Conic Sections
Students will use the distance and midpoint formulas; classify, graph, and write
equations of conics; and solve systems of quadratic equations.
• Evaluate, solve, and analyze mathematical situations using algebraic properties
and symbols.
• Solve systems containing quadratic equations.
• Represent quantitative relationships using mathematical models and symbols.
• Write the equations of conic sections in standard form.
• Specify locations and describe spatial relationships using coordinate geometry.
• Graph conic sections.
• Write the equations of functions when given the graph or information about the
graph.
Chapter 12 Probability and Statistics
Students will learn to compute the number of ways an event can happen, how to
calculate and use probabilities, and how to expand binomials.
• Calculate the number of possible outcomes.
• Use the fundamental counting principle to compute the number of ways an event
may occur.
• Use permutations to compute the number of ways an event may occur.
• Use combinations to compute the number of ways an event may occur.
• Expand a binomial using the Binomial Theorem.
• Find the probability of an event.
• Find geometric probabilities.
• Find probabilities of unions and intersections of 2 events.
• Use complements to find the probability of events.
• Find the probability of independent and dependent events.
• Evaluating series
• Use sigma notation to express sums.
Chapter 13 Trigonometry
Students will learn to evaluate trigonometric functions and inverse trigonometric
functions and to find side lengths, angle measures, and areas of triangles.
• Use patterns, relations, and functions to represent mathematical situations.
• Express angle measure in degrees or radians when given the trigonometric value.
• Represent quantitative relationships using mathematical models and symbols.
• Solve real world problems using the methods for right triangle and general
trigonometric equations.
• Calculate the exact values of the sine, cosine, and tangent functions.
• Evaluate the trig functions for an angle of a right triangle.
• Evaluate the trig functions for an angle of a 45-45-90 or a 30-60-90 triangle.
• Evaluate the trig functions for an angle in standard position.
• Solve triangles.
• Solve right triangles.
• Apply the ratios of 45-45-90and 30-60-90 triangles.
• Work with the units and processes of the measurement of rotational angles.
• Convert angle measurements between radians and degrees.
• Calculate the exact values of the sine, cosine, and tangent angles for the special
angles of the unit circle.
• Calculate the exact values of inverse trigonometric functions.
• Solve simple trigonometric equations.
• Apply the Law of Sines and the Law of Cosines to solve oblique triangles.